European matches have had an uncanny knack of restoring a sense of reality to Scottish clubs in an often striking fashion in recent times. Yet Celtic, buoyant in the early weeks of the Scottish Premierleague season, continued their winning form last night and significantly bolstered their hopes of progressing from Group F in the process.

A 36th minute Kenny Miller penalty was enough in a game that Celtic made unnecessarily hard work of as Copenhagen offered little attacking threat and failed to impose their physical advantage. Of utmost importance to the Celtic manager Gordon Strachan is that Benfica visit Glasgow next month for the club's Champions League match with his team in a strong position to qualify for the last 16.

Strachan hailed the "excellent" news from Lisbon of Manchester United's victory over his team's next opponents, with the former Coventry and Southampton manager hoping his former club can embark on a winning streak against Celtic's nearest challengers for qualification.

Personal issues between Strachan and Sir Alex Ferguson will be forgotten for the meantime at least although whether personal messages of good luck will be exchanged remains open to question.

"I am just hoping Man United go out and win every game now, apart from when they play ourselves," said Strachan. "The Celtic players are happy tonight, the fans are happy and hopefully we have made the people of Scotland happy with this result."

Celtic's pre-match optimism was tempered by the absence of their Dutch striker, Jan Vennegoor of Hesselink, who failed to recover from the ankle injury sustained during Saturday's win over Rangers.

Nonetheless Strachan was unlikely to alter his ambition of making a meaningful impact on Europe's premier club competition because of the loss of a key player.

The Celtic manager was hurt by the club's embarrassing exit at the qualifying stage last year and is determined to build on his apparently seamless introduction to Scottish football by achieving Champions League success.

This was only Copenhagen's second ever appearance in the group phase of this competition but they defended with aplomb throughout the opening exchanges. The patience and concentration emphasised pre-match by Strachan were therefore valuable virtues for home players and supporters alike as the Danish champions competently dealt with what Celtic had to offer.

But Michael Gravgaard's clumsy challenge on Shunsuke Nakamura as the Japan international sought to skip past him inside the penalty area, nine minutes before the interval, was crucial in lifting the edginess beginning to descend on Parkhead.

Miller made no mistake from the spot and only a brilliant point-blank save from Jesper Christiansen prevented Miller from doubling the advantage moments later. During a low-key second period, Christiansen, the former Rangers goalkeeper, used his feet to save smartly from the ever-busy Miller but Hjalte Norregaard reminded home fans of the slenderness of Celtic's lead when he forced Artur Boruc into action from 20 yards.

The referee Florian Meyer resisted two claims from Celtic for another, clinching, penalty but Strachan's men held firm. The Copenhagen manager, Stale Solbakken, was not overly downhearted by his side's display ahead of successive matches against Manchester United.

He said: "Celtic deserved their victory. I am a little bit disappointed with our offensive performance but I am pleased with the way we handled the atmosphere. I am just thinking about our next game but the group is still a very open affair."